The recent crowd size debate, (if we can call this a debate), on the inauguration reminded me of something that happens at every demonstration in France. The estimations of the number of demonstrators, according to the police, and according to the organisers, are very different, with a ratio as large as 1 to 10.
Here is a 6/14/16 Le Monde article (in French) about this. It concerns a demonstration about the last labor legislation; the police said there were 125,000 demonstrators, while the organizers (unions) said there were 1,300,000 demonstrators, (1.3 million, there is more than a factor 10 between their estimations, I did not type too many zeros).
Question: What are the different techniques employed to estimate the size of a crowd? Who uses them?
I am not looking for a visually vague answer like a "picture from above". If it is with a picture from above, what do we do with this picture? Are the people counted by hand in a small area and then an extrapolation is made? Is this area representative? Are pictures taken at different moments considered? Is the time the crowd needs to pass a given point considered?